Kinetics of laser-induced melting of thin gold film: How slow can it get?

Melting is a common and well-studied phenomenon that still reveals new facets when triggered by laser excitation and probed with ultrafast electron diffraction. Recent experimental evidence of anomalously slow nanosecond-scale melting of thin gold films irradiated by femtosecond laser pulses motivates computational efforts aimed at revealing the underlying mechanisms of melting. Atomistic simulations reveal that a combined effect of lattice superheating and relaxation of laser-induced stresses ensures the dominance of the homogeneous melting mechanism at all energies down to the melting threshold and keeps the time scale of melting within ~100 picoseconds. The much longer melting times and the prominent contribution of heterogeneous melting inferred from the experiments cannot be reconciled with the atomistic simulations by any reasonable variation of the electron-phonon coupling strength, thus suggesting the need for further coordinated experimental and theoretical efforts aimed at addressing the mechanisms and kinetics of laser-induced melting in the vicinity of melting threshold.

growth of spherical liquid regions cannot be expected to be valid up to T * , when the critical radius rc decreases down to less than a nanometer, Fig. S1B, and the distance the melting front propagates during the melting time of = 10 ps is less than 5 nm. Nevertheless, the kinetics of a more complex melting process revealed in the MD simulations, where a simultaneous formation of a large number of interconnected small liquid regions within the entire superheated volume is observed (10,13,14), is found to still be reasonably well described by the classical nucleation theory.    snapshots are from a TTM-MD simulation performed with g(Te) from Ref. (29). The atoms that belong to the liquid phase are blanked, and the remaining atoms are colored according to the local order parameter, with color variation from blue to red for the local order parameter ranging from 0.04 to 1.
At an absorbed energy density of 0.2 MJ/kg, which is about 6% below the threshold for complete melting, the total number of atoms in the regions that remain crystalline decreases until about 2 ns, and then starts to increase, fig. S5A. This observation can be explained by the disintegration of the crystalline layers into separate regions during the first several hundreds of picoseconds after the laser pulse, fig. S4. The crystalline regions with effective diameters below * =   Tables of the melting times, electron-phonon coupling parameters, and electron temperature predicted in the TTM-MD simulations and obtained from the ultrafast electron diffraction experiments (22), tables S1, S2, and S3. Table S1. The values of the melting times and electron-phonon coupling parameter predicted in the TTM-MD simulations and obtained from the ultrafast electron diffraction experiments (22).
Notation: ε -energy density deposited by the laser pulse; εm -theoretical threshold energy density for complete melting of the Au film; and -the times of the start and end of the melting process, defined as times when the fraction of atoms that belong to the liquid phase reaches the levels of 10% and 98%, respectively; -time of melting reported in Ref. (22).
Exp. (22) , ps , ps g from (22) Table S3. The maximum values of Te and the values of Te at the end of the melting process in simulations performed using constant values of g suggested in Ref. (22). The values of g are outlined by the blue box in Fig. 9.
ε, MJ/kg g from (22) where the electron temperature dependence of the electron heat capacity and electron-phonon where F(x) is the Fowler function (85,86), is the reflectivity at a given laser wavelength, = 120 A cm K is the Richardson coefficient, is the elementary charge, and are material-dependent coefficients, which correspond to the two-and three-photon emission, Here, ( ) − is the chemical potential that accounts for the significant change in the effective .

(S5)
The total electron emission from each of the two surfaces of the film is = + + .
Since the optical penetration depth is comparable with the film thickness and the film is uniformly heated by the laser pulse, the emission from the front and back surfaces of the film can be assumed to be approximately the same. Thus, the total electron current density calculated in the simulation is = 2 . The corresponding numbers of emitted electrons per unit volume of the Au film per unit time are calculated from the continuity equations, As discussed in (88), each thermionically emitted electron on average carries an energy of + − ( ) + . Thus, the energy loss due to thermionic emission is and the total energy loss term present in the TTM equation for Te can be written as